标题： AFIRE：针对几何不一致多光谱CT的精确且快速图像重建算法 显示英文标题

标题： AFIRE: Accurate and Fast Image Reconstruction Algorithm for Geometric-inconsistency Multispectral CT

摘要： 对于非线性多光谱计算机断层扫描（CT），当不同X射线能量光谱下的扫描几何结构不一致或不匹配时，准确且快速的图像重建具有挑战性。受此启发，我们提出了一种名为AFIRE的准确且快速的算法来解决适度完整扫描情况下的此类问题。我们发现，涉及的非线性映射在某些特殊点（例如零点）处的导数（梯度）可以表示为由X射线变换（投影矩阵）组成的对角算子（矩阵）与一个小规模矩阵的复合（块乘法）。基于这些见解，并利用简化牛顿方法，从连续、离散和实际应用的角度分别提出了AFIRE算法。在适当条件下，建立了所提出算法的收敛理论。此外，还进行了数值实验，验证了所提出的算法能够准确有效地重建完全几何不一致性双能CT中的基图像，无论是无噪声还是有噪声的投影数据。特别是，该算法在准确性和效率方面显著优于一些最先进的方法。最后，还展示了所提出算法的灵活性和可扩展性。 显示英文摘要

摘要： For nonlinear multispectral computed tomography (CT), accurate and fast image reconstruction is challenging when the scanning geometries under different X-ray energy spectra are inconsistent or mismatched. Motivated by this, we propose an accurate and fast algorithm named AFIRE to address such problem in the case of mildly full scan. We discover that the derivative operator (gradient) of the involved nonlinear mapping at some special points, for example, at zero, can be represented as a composition (block multiplication) of a diagonal operator (matrix) composed of X-ray transforms (projection matrices) and a very small-scale matrix. Based on the insights, the AFIRE is proposed respectively from the continuous, discrete and actual-use perspectives by leveraging the simplified Newton method. Under proper conditions, we establish the convergence theory of the proposed algorithm. Furthermore, numerical experiments are also carried out to verify that the proposed algorithm can accurately and effectively reconstruct the basis images in completely geometric-inconsistency dual-energy CT with noiseless and noisy projection data. Particularly, the proposed algorithm significantly outperforms some state-of-the-art methods in terms of accuracy and efficiency. Finally, the flexibility and extensibility of the proposed algorithm are also demonstrated.